Modeling Open Channel Fluid Flow Past a Trapezoidal Cross-section with a Segment Base having Lateral Inflow Channel

Floods in flood-stricken areas have been a major threat to the survival of lives and livelihoods in various aspects. For instance, increased pot-holes, road disconnection and tearing off as well as bridges being carried away have led to increased cases of accidents leading to loss of lives. This has led to Government over-stretching budgetary allocations to cater for maintenance and repair of roads and bridges. This study has developed a model for fluid flow past an open channel with a trapezoidal cross-section with a segment base having lateral inflow channel. The turbulent formation between the lateral inflow channel and the main channel are assumed to be negligible and hence the flow is laminar. The model equations governing the fluid flow are non-dimensionalized and solved using finite-difference method. The numerical values are simulated using Matlab software. It is found that an increase in cross-section area of the lateral channel increases the discharge in the main channel leading to an increase in flow velocity. An increase in surface roughness increases shear stress thereby recording a reduced flow velocity. The findings of this study is highly applicable in the design of drainage systems for road construction, sewer building, street drainage, dams, and airport construction in Kenya and elsewhere. Moreover, the designed efficient channels with optimal dimensions are applicable in draining water to hydro-electric power plants where large volumes of high velocity water are required to turn large turbines for electrical processes.